Chapter 26
An Introduction to Chromatographic
Separations
Chromatography permit the scientist to separate closely
related components of complex mixtures. In all
chromatographic separations the sample is transported in
a mobile phase, which may be a gas, a liquid, or a
supercritical fluid. This mobile phase is then forced
through an immiscible stationary phase, which is fixed in
place in a column or on a solid surface. The two phases
are chosen so that the components of the sample
distribute themselves between the mobile and stationary
phase to varying degrees.
Classification of Chromatographic Methods
Chromatographic methods can be categorized in
two ways. The first classification is based upon
the physical means by which the stationary and
mobile phases are brought into contact. In
column chromatography, the stationary phase is
held in a narrow tube through which the mobile
phase is forced under pressure. In planar
chromatography, the stationary phase is
supported on a flat plate or in the interstices of a
paper; here, the mobile phase moves through the
stationary phase by capillary action or under the
influence of gravity.
Classification of Chromatographic
Methods
A more fundamental classification of
chromatographic methods is one based upon
the types of mobile and stationary phases and
the kinds of equilibria involved in the transfer
of solutes between phases. Three general
categories of chromatography: (1) liquid
chromatography, (2) gas chromatography, and
(3) supercritical-fluid chromatography. The
mobile phases in the three techniques are
liquids, gases, and supercritical fluids
respectively.
Elution Chromatography on Columns
Elution involves washing a species through a
column by continuous addition of fresh solvent.
The sample is introduced at the head of a
column, whereupon the components of the
sample distribute themselves between the two
phases. Introduction of additional mobile phase
(the eluent) forces the solvent containing a part
of the sample down the column, where further
partition between the mobile phase and fresh
portions of the stationary phase occurs.
Chromatograms
If a detector that responds to solute
concentration is placed at the end of the
column and its signal is plotted as function of
time (or of volume of the added mobile phase),
a series of peaks is obtained. Such a plot, called
a chromatogram, is useful for both qualitative
and quantitative analysis. The positions of
peaks on the time axis may serve to identify the
components of the sample; the areas under the
peaks provide a quantitative measure of the
amount of each component.
MIGRATION RATES OF SOLUTES
The effectiveness of a chromatographic column
in separating two solutes depends in part upon
the relative rates at which the two species are
eluted. These rates are determined by the
magnitude of the equilibrium constants for the
reactions by which the solutes distribute
themselves between the mobile and stationary
phases.
Distribution Constants
The distribution equilibria involved in chromatography
involve the transfer of an analyte between the mobile
and stationary phases.
Amobile
Astationary
The equilibrium constant K for this reaction is called
the distribution constant, the partition ratio, or the
partition coefficient,
K = cS/cM
where cs is the molar concentration of the solute in the
stationary phase and cM is its molar concentration in the
mobile phase. K is constant over a wide range of solute
concentrations.
Retention Time
The time it takes after sample injection for the analyte
peak to reach the detector is called the retention time
and is given the symbol tR. The time tM for the
unretained species to reach the detector is called the dead
time. The rate of migration of the unretained species is
the same as the average rate of motion of the mobile
phase molecules. The average linear rate of solute
migration  is
 = L/tR
where, L is the length of the column packing. The
average linear rate of movement u of the molecules of
the mobile phase is
u = L/tM
Where tM, the dead time.
The Rate of Solute Migration: The Retention Factor
The retention factor, or capacity factor, is an important
parameter that is widely used to describe the migration
rates of solutes on columns. For a solute A, the retention
factor k`A is defined as
k`A = KAVS/VM
where KA is the distribution constant for the species A.
k`A = (tR - tM )/tM
tR and tM are readily obtained from a chromatogram.
When the retention factor for a solute is much less than
unity, elution occurs so rapidly that accurate
determination of the retention times is difficult. When
the retention factor is larger than perhaps 20 to 30,
elution times become inordinately long. Ideally,
separations are performed under conditions in which the
retention factors for the solutes in a mixture lie in the
range between 2 and 10.
Relative Migration Rates: The selectivity Factor
The selectivity factor  of a column for the two species
A and B is defined as
 = KB/KA
where KB is the distribution constant for species B and
KA is the distribution constant for species A.  is always
greater than unity. A relationship between the selectivity
factor and retention factors:
 = k`B/k`A
Where k`B and k`A are the retention factors. An
expression for the determination of  from an
experimental chromatogram:
(tR) B  tM
 
(tR ) A  tM
Methods for Describing Column Efficiency
Two related terms are widely used as quantitative
measures of chromatographic column efficiency:
(1) plate height H and (2) plate count plates N.
The two are related by the equation
N = L/H
where L is the length (usually in centimeters) of
the column packing. The efficiency of
chromatographic columns increases as the plate
count becomes greater and as the plate height
becomes smaller.
Methods for Describing Column Efficiency
A chromatographic column is made up of
numerous discrete but contiguous narrow layers
called theoretical plates. At each plate,
equilibration of the solute between the mobile
and stationary phase was assumed to take place.
Movement of the solute down the column was
then treated as a stepwise transfer of
equilibrated mobile phase from one plate to the
next.
Plate Height
The plate height H is given by
H = 2/L
L carries units of centimeters and 2 units of
centimeters squared; thus H represents linear
distance in centimeters. The plate height can be
thought of as the length of column that contains
a fraction of analyte that lies between L-  and
L. Because the area under a normal error curve
bounded by  is about 68% of the total area, the
plate height, as defined, contains approximately
34 % of the analyte.
The Experimental Evaluation H and N
N can be calculated from two time measurements
tR and W; to obtain H, the length of the column
packing L must also be known. Another method
for approximating N, is to determine W1/2, the
width of peak at half its maximum height. The
plate count is then given by
N = 5.54(tR/ W1/2)2
The plate count N and the plate height H are
widely used in the literature and by instrument
manufactures
as
measures
of
column
performance.
The Effect of Mobile-Phase Flow Rate
The magnitude of kinetic effects on column
efficiency depends upon the length of time the
mobile phase is in contact with the stationary
phase, which in turn depends upon the flow
rate of the mobile phase. Efficiency studies
have generally been carried out by determining
H as a function of mobile-phase velocity u.
Relationship between Plate Height
and Column Variables
The van Deemter equation can be written in the form
H = A + B/u + Cu
= A + B/u + (Cs + CM)u
where H is the plate height in centimeters, u is the linear
velocity of the mobile phase in centimeters per second,
and the quantities A, B, and C are coefficients related to
the phenomena of multiple flow paths, longitudinal
diffusion, and mass transfer between phases, respectively.
The C coefficient can be broken into two coefficients,
one related to the stationary phase (Cs) and one related to
the mobile phase (CM). The van Deemter equation
contains terms linearly and inversely proportional to, as
well as independent of, the mobile phase velocity.
The Multipath Term(A)
Zone broadening arises in part from the
multitude of pathways by which a molecule (or
ion) can find its way through a packed column.
The length of these pathways may differ
significantly; thus, the residence time in the
column for molecules of the same species is
also variable. Solute molecules then reach the
end of the column over a time interval, which
leads to a broadened band. This effect which is
called eddy diffusion, is directly proportional to
the diameter of the particles making up the
column packing.
The Longitudinal Diffusion Term (B/u)
Longitudinal
diffusion
in
column
chromatography is a band broadening process
in which solutes diffuse from the concentrated
center of a zone to the more dilute regions
ahead of and behind the zone center. The
longitudinal diffusion term is directly
proportional to the mobile-phase diffusion
coefficient
DM.
The
contribution
of
longitudinal diffusion is seen to be inversely
proportional to the mobile phase velocity.
Mass-transfer Coefficients (Cs and CM)
The need for the two mass-transfer coefficients Cs and
CM arises because the equilibrium between the mobile
and the stationary phase is established so slowly that a
chromatographic column always operates under
nonequilibrium conditions.
Effect of Mobile-Phase Velocity
Fig. 26-10 provides the quality of the fit of the van
Deemter equation. The upper curve was obtained from
a numerical fit of the van Deemter equation to the data.
The lower plots in the figure also show the contribution
of the longitudinal diffusion, and the masstransfer
effects.
Methods for Reducing Zone Broadening
Two important controllable variables that affect
column efficiency are the diameter of the
particles making up the packing and the diameter
of the column. To take advantage of the effect of
column diameter, narrower and narrower columns
have been used in recent years. With gaseous
mobile phases, the rate of longitudinal diffusion
can be reduced appreciable by lowering the
temperature and thus the diffusion coefficient DM.
The consequence is significantly smaller plate
heights at low temperatures.
Column Resolution
The resolution Rs of a column provides a quantitative
measure of its ability to separate two analytes. Column
resolution is defines as
Z
2 Z
2[(tR ) B  (tR ) A]
Rs 


WA / 2  WB / 2 WA  WB
WA  WB
It is evident from Fig.26-12 that a resolution of 1.5
gives an essentially complete separation of the two
components, whereas a resolution of 0.75 does not. At a
resolution of 1.0, zone A contains about 4% B and zone
B contains a similar amount of A. At a resolution for
1.5, the overlap is about 0.3% . The resolution for a
given stationary phase can be improved by lengthening
the column, thus increasing the number of plates.
The Effect of Retention and Selectivity Factors on
Resolution
Relationship between the resolution of a column and
the retention factors k`A and k`B for two solutes, the
selectivity factor , and the number of plates
Rs 
N
k'
(  1)(
)
4
1 k '
1 2 1 k' 2
N  16 Rs(
)(
)
 1 k'
2
Where k’ is the average of k’A and k’B
APPLICATIONS OF
CHROMATOGRAPHY
Chromatography has grown to be the
premiere method for separating closely
related chemical species. In addition, it
can be employed for qualitative
identification
and
quantitative
determination of separated species.
Qualitative Analysis
A chromatogram provides only a single piece of
qualitative information about each species in a
sample, namely, its retention time or its position
on the stationary phase after a certain elution
period. It is a widely used tool for recognizing
the presence or absence of components of
mixtures containing a limited number of
possible species whose identities are known.
Positive spectroscopic identification would be
impossible
without
a
preliminary
chromatographic separation on a complex
sample.
Quantitative Analysis
Chromatography
can
provide
useful
quantitative information about the separated
species. Quantitative column chromatography
is based upon a comparison of either the height
or the area of the analyte peak with that of one
or more standards. For planar chromatography,
the area covered by the separated species
serves as the analytical parameter. If conditions
are properly controlled, these parameters vary
linearly with concentration.
Analyses Based on Peak Height
The height of a chromatographic peak is
obtained by connecting the base lines on either
side of the peak by a straight line and measuring
he perpendicular distance from this line to the
peak. This measurement can ordinarily be made
with reasonably high precision. Accurate results
are obtained with peak heights only if variations
in column conditions do not alter the peak
widths during he period required to obtain
chromatograms for sample and standards. The
variables that must be controlled closely are
column temperature, eluent flow rate, and rate
of sample infection.
Analyses Based on Peak Areas
Peak areas are a more satisfactory analytical
variable than peak heights. On the other hand,
peak heights are more easily measured and, for
narrow peaks, more accurately determined.
Most modern chromatographic instruments are
equipped with digital electronic integrators that
permit precise estimation of peak areas. If such
equipment is not available, manual estimate
must be made. A simple method, which works
well for symmetric peaks of reasonable widths,
is to multiply the height of the peak by its width
at one half the peak height.
Calibration and Standards
The most straightforward method for
quantitative chromatographic analyses
involves the preparation of a series of
standard solutions that approximate the
composition
of
the
unknown.
Chromatograms for the standards are then
obtained and peak heights or areas are
plotted as a function of concentration. A
plot of the data should yield a straight line
passing through the origin.
The Internal Standard Method
The
highest
precision
for
quantitative
chromatography is obtained by use of internal
standards because the uncertainties introduced by
sample injection are avoided. In this procedure, a
carefully measured quantity of an internal
standard substance is introduced into each
standard and sample, and the ratio of analyte to
internal standard peak areas (or heights) serves as
the analytical parameter. For this method to be
successful, it is necessary that the internal
standard peak be well separated from the peaks of
all other components of the sample.